Final answer:
To write .09 repeating as a fraction in lowest terms, it can be simplified to 1/11.
Step-by-step explanation:
To write .09 repeating as a fraction in lowest terms, we can represent it using variables. Let x = .09 repeating. If we multiply both sides of this equation by 100, we get 100x = 9.99 repeating. Next, subtracting x from 100x gives us 99x = 9. Expressing 9 as a fraction, we have $rac{9}{1}$. Dividing both sides of the equation by 99, we find that x = $rac{9}{99}$, which simplifies to $rac{1}{11}$.
Learn more about Converting a repeating decimal to a fraction